One night early last month he was onstage at the Orpheum Theatre in Los Angeles, playing his guitar. In his capacity as the musical director of the Plastic Ono Band, the conceptual group formed in 1969 by his mother, Yoko Ono, and father, John Lennon, his duties also involved wrangling a menagerie of guest performers: Iggy Pop, Paul Simon, the actor Vincent Gallo, the Wu-Tang Clan rapper RZA. The occasion was a gala concert being held in the week leading up to what would have been his father’s 70th birthday.

'It was really difficult,’ Lennon, 35, acknowledges of his multi-faceted organisational role. 'But also, in a way, that show is very succinct. Because it’s about my mum being the queen of the board. And all I have to do is create everything to glorify her. It’s easy for me to do that.’

Having co-produced Ono’s 2009 album Between My Head and the Sky and released it on his own record label, Chimera Music, and, long before that, having dropped out of Columbia University to go on tour with her, he feels that 'we know our [places in our] relationship respectively.’

But at the Orpheum there was a second queen on the board: Lady Gaga, another special guest, tottered onstage.

'She’s one of the nicest superstars I’ve ever met,’ says Lennon, a man who knows about rubbing shoulders with the rich, famous and talented. His girlfriend, the model Charlotte Kemp Muhl, picks up the story: 'Gaga was killing it as always and everyone was standing on their feet and screaming. And Yoko was looking at this and she was like, “Hmm…” She was not to be outdone! So she climbed all over the piano – and she’s 77! And Gaga climbed up after her. They both started rolling around and singing upside down on top of the piano. It was amazing.’

Was it a proud moment for Lennon? Or was he thinking, 'Oh, for God’s sake, Mum’?

'I was proud,’ he smiles. 'But I was just a little bit scared, too. It was a grand piano and it was slippery and they were both in heels. They were both wearing fine silk fabrics. I just didn’t know what was going to happen. Should I catch her or should I cue the end of the song? What could happen now, other than something terrible?’ He gave the rest of the musicians the signal: 'OK, let’s just end it.’

Kemp Muhl, 23, is also Lennon’s partner in his own musical project, the Ghost of a Saber Tooth Tiger (GOASTT), named after a short story that she wrote. Raised in Atlanta, Georgia, she began modelling at the age of 13. At 16 she was reportedly the youngest model to appear on the cover of Harpers & Queen. She is currently contracted to the make-up brand Maybelline, but dismisses most of her other modelling work – it’s 'depressingly easy’ – and she says she does it only to help pay for her musical adventures. Kemp Muhl and Lennon met backstage at the Coachella music festival in California six years ago.

Their itinerant lifestyles meant that they courted long-distance, via letter and emails. Their formative love of the written word bloomed into a musical partnership.

Just as John Lennon fell in love with Yoko Ono and they made beautiful – and often singularly self-involved – music together, so Sean Lennon has collaborated with Kemp-Muhl to create beautiful – and occasionally inward-looking – songs. But there, they insist, the comparison must end.

'My parents are a Catholic Republican military family from Georgia in the south,’ Kemp Muhl says. 'Completely the opposite of his family. So his heritage was not exactly a bonus.’

'Charlotte hadn’t even heard Strawberry Fields Forever when I met her,’ Lennon says. 'And she knew nothing about my mum. Her parents thought I was just a delinquent, by virtue of association with the famous hippie delinquents. So it was nice because it was like a bridging of gaps and a collision of galaxies.’

Lennon and Kemp Muhl share a four-floor townhouse in Greenwich Village, New York, which also has space for the studio where, as the GOASTT, they recorded their debut album, Acoustic Sessions, as well as the offices of Chimera and a top-floor 'painting studio’. One account puts its value at $5.49 million. Having inherited a reported $60 million from his father’s estate, Lennon can afford it.

Lennon insists that the cross-generational comparisons are wrong-headed in other ways, too.

'There couldn’t be someone less like my mum than Charlotte,’ he says with quiet firmness. Although he was born and raised in America and has an American accent, he has an English diction ('mum’ not 'mom’) that gets stronger the more beer he drinks. He also develops more of his father’s nasal twang as the night wears on. Curious, given that his father was killed when he was only five. But at the same time, not curious. Lennon has grown up with his father’s words and speech, music and iconography around him, all the time, every day.

Sean Lennon grew up in New York, where his father and mother set up home after the demise of the Beatles in 1970. When Sean was born in 1975, John Lennon opted out of the music business. As he is heard to say in a recording featured in a new documentary, LennonNYC (which premiered at last month’s London Film Festival), he felt guilty that he had been absent, touring the world with the Beatles, during the infancy of his elder son, Julian (born to his first wife, Cynthia, in 1963).

He resolved to be there for his and Ono’s baby. In the words of an associate who is quoted in the documentary, John Lennon cancelled his subscription to the music industry magazine Billboard, tuned his radio dial to 'easy listening’, learnt to bake bread, and concentrated on being a father and house husband. While Ono went 'out to work’ – that is, to the office downstairs from their huge apartment complex in the Dakota building in Manhattan – to keep her and her husband’s artistic life ticking over, Lennon was a stay-at-home father whose proudest achievement was teaching his son to swim.

Sean Lennon acknowledges the richness of those early years, 'but five years is a short time. I wish I had had maybe 10. But I am lucky. I’m lucky to have had a father who paid attention. I think it helped me psychologically. It’s given me a level of confidence.’

At the age of 12, he told his mother he wanted to go to school abroad. Did he yearn to escape what one imagines is the terribly long shadow cast by his father’s murder outside the building in which Sean and Ono continued to live?

'No,’ he says. 'It was about not being American. I really felt that America, no matter how rich and powerful, was a provincial country… I wanted to have an international education. I wanted to feel global in my understanding of the world. That sounds really pretentious,’ he smiles, 'but that’s the kind of 12-year-old I was.’

His first choice was England. 'But the school that I applied to held a press conference about me going to that school. Then I thought, f*** that – there was too much weird press attention for me in England.’ So he went to Switzerland, where he attended the exclusive Le Rosey boarding school. 'Switzerland was a great way to be anonymous,’ he says, adding that he still managed to acquire the English education he sought. 'I did O-levels and GCSEs. And I learnt to pee out the window.’

'You also had a really nice tryst with a French maid,’ Kemp Muhl chips in. Lennon shakes his head at his indiscreet girlfriend. 'It made him a man,’ she continues blithely.

In spite of being asked about his father all his life, Sean is happy to talk about John. He has supported his mother as she has undertaken the recent repackaging and reissuing of all his father’s post-Beatles records, and even drew new cover art for Double Fantasy, the album Lennon and Ono were making when he was killed. But he is also notably mindful to steer the conversation back to Ono as often as possible. Knowing as well as anyone the antipathy she inspires in certain quarters, he will praise and defend her to the last. 'It’s so funny – even the other Beatles had said that she didn’t break up the Beatles. And still the fans are like [boorish yob voice], “You broke up the Beatles!”’

He is unstinting in his support of Ono, as an artist and as a mother. 'I think a lot of kids are ignored,’ he says. 'Even if their parents are there and are talking and interacting, their real feelings are ignored. Whereas my mum was always very open with me and I felt comfortable talking about anything with her. A lot of people say that a parent should be a parent and not your friend. But I have to admit, I was brought up in that way – just being friends with my mum. It was really good for me because it makes me able to have friendships with people. I’m not closed up.’

From an early age, those friendships were formed in gilded circles. He is close to the rest of the Beatles inner circle. George Harrison’s son, Dhani, who has his own new band, Fistful of Mercy, is a long-time friend. Of Paul McCartney he says, 'I’m just so excited when I’m around him. It’s like when you see a white buffalo and you just hold your breath – you’re just hoping that it’s not going to end. Because,’ he adds quietly, 'it’s the closest I can come to hanging out with my dad. Every second I’ve ever spent with Paul has been really meaningful to me. He was my dad’s best mate for a long time. And my dad didn’t have many friends, you know?’

Way back when, Sean Lennon also knew Michael Jackson (he had sleepovers at Neverland). He has known Rashida Jones, the daughter of Jackson’s producer Quincy Jones, for a long time. A former girlfriend is Bijou Phillips, the model/actress daughter of John Phillips of the Mamas & the Papas. The musician and producer Mark Ronson has been a 'mate’ since 'they were little toddlers,’ Kemp Muhl says. 'And Sean was kind of a bully with him when they were kids – Sean would always tie him up and lock him in a closet. And now he has to definitely look up to Mark, so the tables have turned.’

Lennon is ambivalent about Nowhere Boy, the biopic of his father’s pre-Beatles life in Liverpool. A year after its British premiere, the film has just opened in the US, its release timed to coincide with the concerts, memorials and marketing events tied to what would have been his father’s 70th birthday. He says he has seen it but, poking his glasses up the bridge of his nose and screwing up his face, adds, 'I can’t buy into the fantasy. I’m sure Nowhere Boy is a great film. But I personally can’t watch somebody younger than me and believe that it’s my dad. My dad, in my mind at least, is a father figure. Not a teenager.’

He felt a similar sense of dislocation when he visited the John Lennon Museum outside Tokyo. The last installation is the White Room, a recreation of the space in the Dakota where Lennon played the piano and wrote. I toured the exhibit last year in the company of Yoko Ono. She cried when we reached that final section of the museum. But Sean doesn’t get it: 'Do I have any sense or connection that that’s the White Room? I don’t. It just feels obviously a contrivance.’

Sean Lennon has little time for the blinkered idolatry that attends his father. In July he posted a picture on Twitter of Lady Gaga playing John Lennon’s white piano – the one from the Imagine video – in the Dakota. It caused outrage among John Lennon fans, not least because Gaga was clad in only a leotard and fishnet stockings. Sean posted quick and impassioned ripostes.

'I leapt to Gaga’s defence because I can sympathise – I receive so much ridicule for so many meaningless, pointless events that I’m used to it,’ he sighs, pointing out that it is not unusual for random strangers to assail him with, as he puts it, 'hey f*** you, you’re John Lennon’s son, who the f*** do you think you are?’

Furthermore, he says agitatedly, 'It’s my mum’s piano. If you look at the piano it says for yoko, happy birthday, love john. And it’s the piano on which I learnt to play. It’s the piano in our house and everyone who comes there plays it. It’s not some crazy, sacred museum object that we’re going to just let rot in a cage. I don’t want to sound like I’m not respectful of a very incredible legacy. But I don’t feel that playing a piano is disrespectful to the legacy.’

Even if the player is wearing only fishnets?

'Yeah! And frankly the way Gaga was dressed was a lot more modest than the way my mum dressed. She wouldn’t wear clothes at all…’

The night after our interview the GOASTT perform at the Roundhouse Studio in Camden, north London. Charlotte Kemp Muhl proves herself more than a pretty face by playing guitar and percussion, and harmonising elegantly with Lennon. He, dapper in his bowler hat with a feather sticking out, has a winsome, delicate voice and a keen way with a melody.

Afterwards there is a tiny gathering in the cupboard-sized dressing-room. Winding down after a hectic few weeks – after Los Angeles, the GOASTT played in Paris during Fashion Week, where Kemp Muhl also had some modelling commitments for Maybelline – they were glad to be just playing their own shows. Next stop: Tokyo, where Lennon had agreed to write some music for a Honda advertisement. 'We’re prostituting ourselves!’ Kemp Muhl piped up.

Some critics have been scornful of the GOASTT, but Lennon, who has made four solo albums, is unabashed. He and Kemp Muhl insist that they inspire each other. An accomplished guitarist, pianist and producer, he encourages her raw musical talents. A former member of America’s Poetry Society (Lennon says she had 'written three novels by the age of 12’), she acts as a catalyst for his lyrics. 'Sean was a lot shyer lyrically in his solo career,’ she says. 'I think because his father was such a great lyricist it was hard to tackle that.’ Acoustic Sessions is sparse and minimal, brimming over with lyrical wordplay.

For his part, Lennon wants the GOASTT to pay its own way. 'Even though I have a trust fund I couldn’t just make whatever [music] I want for the rest of my life and be fine. The monies are not infinite. If I just made records and toured and toured and toured and was just burning money, eventually I’d run out. So no, I can’t do that.’

On December 8, the 30th anniversary of John Lennon’s murder, Yoko Ono will be in Tokyo, hosting the annual fundraising Dream Power concert she instituted in his memory. Sean Lennon says he wanted to be there this year, but unfortunately – or perhaps fortunately – he will be otherwise engaged, touring France with the GOASTT.

'I look out for my mum on the date,’ he says. 'I always call her to make sure she’s all right. But there isn’t a day goes by that I don’t think about my dad anyway. It’s slightly more… sentimental on that day. But I’m more worried about her.’

Will the fact that this year is the 30th anniversary make it more difficult than normal? 'What can I say?’ Lennon shrugs. 'It’s amazing how long ago it seems. But also how close it seems, in many ways. Life is an amazing journey, let’s put it that way. And it’s pretty wild.’

The Ghost of a Saber Tooth Tiger album 'Acoustic Sessions’ is out on November 22